Related papers: Schatten classes on compact manifolds: Kernel cond…
We review recent results about heat kernel estimates based on Kato conditions on the negative part of the Ricci curvature.
We generalize some results on compact operators on Hilbert spaces to "compact" operators on some Hilbert right W*-modules. We present in this frame the Schatten decomposition of the compact operators, the trace, the Banach Lp-spaces and…
We extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly…
A map between connected $2$-manifolds has a geometric kernel if it sends a non-contractible simple loop to a null-homotopic loop. While every non-$\pi_1$-injective map between compact surfaces admits a geometric kernel, this generally fails…
We generalize von Neumann's well-known trace inequality, as well as related eigenvalue inequalities for hermitian matrices, to Schatten-class operators between complex Hilbert spaces of infinite dimension. To this end, we exploit some…
We give a necessary and sufficient condition for a set of left invariant metrics on a compact Heisenberg manifold to be relatively compact in the corresponding moduli space.
Motivated by the recent work of Gimperlein and Goffeng on Calder\'on's commutator on compact Heisenberg type manifolds and the related weak Schatten class estimates, we establish the characterisation of $L^p$ boundedness for Calderon's…
Given a compact Lie group $G$, in this paper we give symbolic criteria for operators to be nuclear and r-nuclear on Lp-spaces, with applications to distribution of eigenvalues and trace formulae. Since criteria in terms of kernels are often…
We present a necessary and sufficient condition for the strict positive definiteness of a real, continuous, isotropic and positive definite kernel on a two-point compact homogeneous space. The characterization adds to others previously…
We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1,1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized…
In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tensors of anharmonic oscillators thanks to the knowledge on…
The article investigate the necessary and sufficient conditions for the normalized Bessel-struve kernel functions belonging to the classes $\mathcal{T}_\lambda(\alpha)$ , $\mathcal{L}_\lambda(\alpha)$. Some linear operators involving the…
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…
We show that any set of quotients with fixed Chern classes of a given coherent sheaf on a compact Kaehler manifold is bounded in a sense which we define. The result is proved by adapting Grothendieck's boundedness criterium expressed via…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a…
Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient…
We study strong ratio limit properties of the quotients of the heat kernels of subcritical and critical operators which are defined on a noncompact Riemannian manifold.
In this paper the general spectral properties of linear operators in Banach spaces are studied. We find sufficient conditions on structure of Banach spaces and resolvent properties that guarantee completeness of roots elements of Schatten…
We extend Feichtinger's minimality property on smallest non-trivial time-frequency shift invariant Banach spaces, to the quasi-Banach case. Analogous properties are deduced for certain matrix classes. We use these results to prove that…